ABSTRACT
In opto-and microelectronics, as well as in nanophotonics use is made of sophisticated optical devices with the dimensions of the order of the wavelength of incident light, whose work is described by the non-trivial physical effects, such as multiple scattering on periodic structures (Bragg diffractive gratings), the scattering and diffraction on aperiodic structures (diffractive optical elements (DOE)), the dispersion and non-linear transformation of laser pulses. The effect of these elements can not be predicted on the basis of geometrical optics or scalar diffraction theory, and it is essential to study the propagation of light waves through them using the vector model of diffraction. All this creates a greater need for efficient numerical approaches for modelling the wave propagation of light, if possible taking into account dispersion, scattering, complex interference effects, etc. Also, the use of the vector diffraction model is required when the relevant calculation area is located near or within the optical element. Although analytical solutions of the vector diffraction problem can be obtained for selected objects (sphere, halfplane, cylinder) [1, 2] the boundary conditions on the electromagnetic field for other dielectric structures makes the analytic solution impossible.
